Richardson model description of spin-orbit coupling ‌in superconducting islands

R. Žitko1,2, L. Pavešič1,2

1Jožef Stefan Institute, Jamova 39, Ljubljana, Slovenia

2Faculty of mathematics and physics, Jadranska 19, Ljubljana, Slovenia

Richardson model, first introduced in nuclear physics as a simplified model of nucleon pairing, is also an appropriate description of a small superconducting island with fixed charge. Complex systems composed of interconnected superconducting islands and interacting quantum dots can be modelled using Hamiltonians that can be transformed into the matrix-product-operator form with small matrices that can be efficiently solved using the density matrix renormalization group [1,2]. This approach allows to include without any approximations the effects of both the exchange interaction (Kondo screening and Yu-Shina-Rusinov subgap states) and the charge repulsion (Coulomb blockade, capacitive coupling) [3] and thereby provide reference results for this family of Hamiltonians that are more general than regular quantum impurity problems. The theory results match well the experimental measurements on hybrid semi-super devices [3,4].

I will describe how this approach can be extended to incorporate two further phenomena, the spin-orbit coupling and the proximity effect leading to level-dependent pairing strength [5]. The combination of the two leads to a degeneracy of even and odd-parity ground states in the regime where the external magnetic field becomes strong enough to generate an increasing number of quasiparticles in the superconducting levels with the weakest pairing strength. This manifests as equal spacing of even and odd states in the charge stability diagrams.

1. Luka Pavešič, Daniel Bauernfeind, and Rok Žitko, Phys. Rev. B 104, L241409 (2021)
2. Luka Pavešič and Rok Žitko, Phys. Rev. B 105, 075129 (2022)
3. Juan Carlos Estrada Saldaña, Alexandros Vekris, Luka Pavešič, Peter Krogstrup, Rok Žitko, Kasper Grove-Rasmussen & Jesper Nygård, Nat. Commun. 13, 2243 (2022)
4. Juan Carlos Estrada Saldaña, Alexandros Vekris, Luka Pavešič, Rok Žitko, Kasper Grove-Rasmussen, Jesper Nygård, arXiv:2203.00104
5. Juan Carlos Estrada Saldaña, Luka Pavešič, Alexandros Vekris, Kasper Grove-Rasmussen, Jesper Nygård, Rok Žitko, arXiv:2306.06001